This activity involves rounding four-digit numbers to the nearest thousand.

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Are these statements always true, sometimes true or never true?

Here are two kinds of spirals for you to explore. What do you notice?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

An investigation that gives you the opportunity to make and justify predictions.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

What happens when you round these three-digit numbers to the nearest 100?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Nim-7 game for an adult and child. Who will be the one to take the last counter?

How many centimetres of rope will I need to make another mat just like the one I have here?

Can you find all the ways to get 15 at the top of this triangle of numbers?

This task follows on from Build it Up and takes the ideas into three dimensions!

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

What happens when you round these numbers to the nearest whole number?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

This challenge is about finding the difference between numbers which have the same tens digit.

Got It game for an adult and child. How can you play so that you know you will always win?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?